3/12 ; 1/6 ; 1/3
Adam must first get the least common multiple of each denominator.
12 : 12, 24, 36
6 : 6, 12, 18
3 : 3, 6, 9, 12
12 is the least common denominator.
We, then, multiply each denominator by a number that will produce 12.
12 x 1 = 12
6 x 2 = 12
3 x 4 = 12
Each number multiplied to the denominator must be the number used to multiply each numerator.
3/12 * 1/1 = 3/12
1/6 * 2/2 = 2/12
1/3 * 4/4 = 4/12
Since they now share a common denominator, the numerator will become the basis of the fraction's value. The greater the numerator, the greater the fraction's value.
Fractions in order from least to greatest = 2/12 ; 3/12 ; 4/12
Substitute each fraction with its original fraction:
2/12 ⇒ 1/6 : least
3/12 ⇒ 3/12 : middle
4/12 ⇒ 1/3 : greatest
Well according to the Inscribed Angle Theorem, the angle inscribed in a circle is equal to one-half of its intercepted arc. We can apply that theorem to this problem as well. So the measure of AED = 1/2( arc AD + arc BC). Plug in the numbers and simplify.
AED = 1/2( 62 + 28)
AED = 1/2( 90 )
AED = 45
So the measure of angle AED is B. 45 degrees.
Hope I helped!
Given:
arithmetic progression
a₁ = 3
a₂ = x
a₃ = y
a₄ = 18
Solution:
The arithmetic progression has general formula to determine nth term
a₁ + d(n - 1) = an
a₁ represents first term, d represents difference, n represents number of terms, an represents nth term
First we should find out the value of d, by submitting a₄ to the formula
a₁ + d(n - 1) = an
a₁ + d(4 - 1) = a₄
3 + d(3) = 18
3 + 3d = 18
3d = 15
d = 5
The difference of the sequence is 5
Second, determine x and y
x = a₂
x = a₁ + d(2 - 1)
x = 3 + 5(1)
x = 8
y = a₃
y = a₁ + d(3 - 1)
y = 3 + 5(2)
y = 13
The value of x is 8, the value of y is 13
In 8 years you will be twice as old as your brother.
Right now, your brother is 4 years old, and 4 x 4 is 16, so you are 16.
In two years, your brother would be 6, and you would be 18, making you 3 times as old.
So, in 8 years, your brother will be 12 years old, making you 24. 12 is half of 24.
